Getting to Grips with Poker Pot Odds

投稿者： Matthew Cluff

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People often say that poker is a game of mathematics and probability. In order to play profitably over the long run, knowing and being able to apply the mathematical skill aspect to your game is certainly true!

The strategy involves a part of the game that deals with calculating (1) outs, (2) poker pot odds and (3) your equity in a pot. While the three concepts go hand-in-hand, our main focus in this article will be elaborating on the first two.

What Are Poker Pot Odds?

Poker pot odds take into account the number of “outs” you have (cards that can improve your hand) and relate them to the amount of money you have to call to see another card.

This calculation is used to ultimately determine whether calling to “chase” your draw is a profitable play over the long run. So, when players ask the question, “Are pot odds important?” - the answer is a big, emphatic YES!

Keep in mind that poker is a game that is more about winning over the long-term than over short, individualised sessions. By using the following information on pot odds, you will be able to make many +EV decisions at the tables.

Calculating Pot Odds

How to Read Pot Odds as Percentages, Fractions, and Ratios

If you have a 33% chance of improving your hand, this fraction can be expressed as “1/3”. For every three times you call trying you improve, you’ll make your hand one of those times (on average).

We need to be able to convert these fractions to ratios, though, to be able to relate them to pot odds.

In poker, these odds are expressed in the following format when trying to improve your hand:

Number of times you won’t make your hand
-------------------------------------------------
Number of times you will make your hand

An example of this would be 2:1 (which would be read as “2 to 1” or “2 to 1 odds”).

It can also be expressed as 33% (percentage) = 1/3 (fraction) = 2:1 (ratio).

Poker Pot Odds Formula

Now that we understand ratios regarding the chances of improving our hand, let’s apply the same concept to understanding pot odds.

Let’s suppose there is $50 in the main pot already, and someone bets and additional $50. Now, there’s $100 total in the pot, and you have to call a bet that’s $50.

The pot odds call in this scenario is a ratio of $100 to $50, or 2 to 1 pot odds.

The formula for determining this is as follows:

$ in main pot already + $ put into pot during current betting round
--------------------------------------------------------------------------
$$$ you have to call

For another example, let’s assume there’s already $200 in the main pot. In this betting round Player 1 bets $100, Player 2 calls $100, and now the action is on you.

What are your pot odds?

Using the formula above, we arrive at the following equation: $400:$100 or 4 to 1

($200 in the main pot) + ($200 from this betting round)
--------------------------------------------------------------------------
($100 you have to call)

How Pot Odds Work

The next step in determining whether or not we have the right pot odds to call a bet when on a draw relates the pot odds we’ve calculated to the chances we’ll improve our hand. (We’ll learn how exactly how to calculate our chances of improving in the next section.)

Simply put, though, if our chances to improve to a winning hand are greater than the pot odds we’re getting for a call, then calling becomes the correct, profitable play.

Let’s suppose that we’re playing Hold’em and we have hold 8-7 off-suit. The board reads K-5-6-2 rainbow. Currently, our hand value is extremely weak (8-high), but we do have the chance of making the best possible straight if a 4 or 9 comes on the river.

From a standard deck of 52 playing cards, we know 6 cards of these cards already after the turn (2 in our hand and 4 on the board). Therefore, of the 46 remaining cards in the deck that could come on the river, only 8 of those will improve our hand (four 4’s and four 9's). This calculation can be expressed as a fraction of 8/46.

We can then use this ratio to relate “river cards that will not improve our hand” to “river cards that will improve our hand”:

8 river cards will help us

46 unknown cards – 8 cards that will help us = 38 cards that will not help us

38 cards that will nothelp us : 8 cards thatwillhelp us

38 : 8

4.75 : 1

The ratio of 4.75 to 1 indicates that for every 4.75 times we won’t improve, 1 time we will improve. Therefore, for us to make a profitable call here, we need to have better than 4.75 to 1 pot odds (i.e. $500 in the pot already when facing a $100 bet).

How to Calculate Pot Odds Quickly

It's quite apparent that using the above formula to determine whether or not you have the right odds to call can be a laborious process. However, the good news is that there’s a shortcut to help you out!

This equation is called the “Rule of Two and Four” or the “Rule of Four and Two”. It’s used by poker players around the world to quickly help them determine their approximate chances of improving their hand when they’re on a draw.

Once they’ve done some simple calculations, they can then swiftly relate this information to the pot odds they’re getting and see if it’s profitable to call.

The “Rule of 2 and 4” states that if you multiply the number of outs that you have by 4 with two cards to come, you’ll arrive at the approximate percentage of making your hand by the river.

Similarly, if you multiply the number of outs that you have by 2 with one card to come, you can determine the likelihood of whether or not you’ll hit your draw.

How to Convert Pot Odds to Percentages

Now that we’ve learned how to calculate both pot odds and the chances of improving, it’s time to relate the two together to see if we have the right odds to call.

However, when using the “Rule of 2 and 4”, you’re commonly going to be left with a percentage, whereas when calculating pot odds, you’re going to be left with a ratio (such as 2 to 1, or 3 : 1).

Therefore, it’s important to be able to convert percentages to ratios and vice versa, if you want to swiftly determine if you’re getting the right price or not to call.

Let’s start by learning how to convert percentages to ratios.

PERCENTAGES TO ODDS:

Using the “Rule of 2 and 4”, with 9 outs and 2 cards to come, we have about a 36% chance of improving our hand to a flush. Through a simple calculation, we can deduce that about 64% of the time, we won’t hit our draw.

When converting percentages into a ratio, you should always put them in the following format:

(chance you will not improve your hand) : (chance you will improve your hand)

Using this format would leave us with a ratio of 64 : 36, or about 2 to 1 – a ratio which can be easily compared to our pot odds. The more you practise this process (pot odds vs. percentage), the better you will become at being able to determine the odds of improving your hand.

ODDS TO PERCENTAGES:

Let’s flip that around now and see how we can turn pot odds into percentages. Say someone makes a ½-pot bet, which would give us 3 to 1 on a call. (They bet $50 into a $100 pot. The pot is now $150, and you have to call with $50, giving you 3 to 1 pot odds.)

By turning this ratio into a fraction, we can easily calculate the approximate percentage, as follows:

1 Card To Come

2 Cards to Come

FLOP to TURN

TURN to RIVER

TURN and RIVER

OUTS

HAND EXAMPLES

%

ODDS

%

ODDS

%

ODDS

1

2.13%

45.95 : 1

2.17%

45.08 : 1

4.26%

22.50 : 1

2

Pocket Pair to Set

4.26%

22.47 : 1

4.35%

21.99 : 1

8.42%

10.88 : 1

3

One Overcard

6.38%

14.67 : 1

6.52%

14.34 : 1

12.49%

7.01 : 1

4

Inside Straight Draw

8.51%

10.75 : 1

8.70%

10.49 : 1

16.47%

5.07 : 1

5

One Pair to Two Pair or Set

10.64%

8.40 : 1

10.87%

8.20 : 1

20.35%

3.91 : 1

6

No Pair to Pair (Hold'em)

12.77%

6.83 : 1

13.04%

6.67 : 1

24.14%

3.14 : 1

7

Set to Full-House / 4-of-a-Kind

14.89%

5.72 : 1

15.22%

5.57 : 1

27.84%

2.59 : 1

8

Open-Ended Straight Draw

17.02%

4.88 : 1

17.39%

4.75 : 1

31.45%

2.18 : 1

9

Flush Draw

19.15%

4.22 : 1

19.57%

4.11 : 1

34.97%

1.86 : 1

10

Inside Straight Draw & Two Overcards

21.28%

3.70 : 1

21.74%

3.60 : 1

38.39%

1.60 : 1

11

23.40%

3.27 : 1

23.91%

3.18 : 1

41.72%

1.40 : 1

12

Inside Straight Draw & Flush Draw

25.53%

2.92 : 1

26.09%

2.83 : 1

44.96%

1.22 : 1

13

Open-Ended Straight and Flush Draw

27.66%

2.62 : 1

28.26%

2.54 : 1

48.10%

1.08 : 1

14

29.79%

2.36 : 1

30.43%

2.29 : 1

51.16%

0.95 : 1

15

31.91%

2.13 : 1

32.61%

2.07 : 1

54.12%

0.85 : 1

16

34.04%

1.94 : 1

34.78%

1.88 : 1

56.98%

0.76 : 1

17

36.17%

1.76 :1

36.96%

1.71 : 1

59.76%

0.67 : 1

18

38.30%

1.61 : 1

39.13%

1.56 : 1

62.44%

0.60 : 1

19

40.43%

1.47 : 1

41.30%

1.42 : 1

65.03%

0.54 : 1

20

42.55%

1.35 : 1

43.48%

1.30 : 1

67.53%

0.48 : 1

ODDS TO PERCENTAGES:

Let’s flip that around now and see how we can turn pot odds into percentages. Say someone makes a ½-pot bet, which would give us 3 to 1 on a call. (They bet $50 into a $100 pot. The pot is now $150, and you have to call with $50, giving you 3 to 1 pot odds.)

By turning this ratio into a fraction, we can easily calculate the approximate percentage, as follows:

(price you have to call / price you have to call + money already in the pot)

In this example, the price we have to call is $50. Therefore, the (price we have to call) + (the money already in the pot) would be $50 + $150, giving us a fraction of $50/$200.

50/200 = 0.25 which can easily be converted into a percentage of 25% by multiplying the 0.25 by 100.

This percentage, in relation to your hand strength, means that you would need to have a greater than 25% of winning the hand to call profitably.

Now, if this still seems difficult to you, worry not! The more you practise with calculating odds, the better you get.

Better yet, to further help you, we’re including a chart below with the majority of pot odds out scenarios already calculated for you!

While it’s not imperative to memorise the above chart, using it during practice scenarios or online sessions can help you develop a “feel” for determining your odds in any situations.

From here, you’ll be able to relate your odds to the pot odds and, with relative ease, determine whether or not to call.

When to Call Using Pot Odds

If we can determine the number of outs we have for improving our hand, then by using the above chart, we can easily see the odds in any given situation.

From there, we simply compare these odds to our pot odds. If your ODDS OF IMPROVING are better than the POT ODDS, then you have the correct pot odds to call.

To put it in even simpler terms, when comparing the numbers in your ratio, if the one on the left of your POT ODDS ratio is greater than the one on the left of your ODDS OF IMPROVING ratio - you should call!

To illustrate this point, let’s use this brief example à

HAND EXAMPLE #2:

You have 6 outs and only the river card to come. There’s $500 in the main pot, and you’re facing a $100 bet.

Do you have the correct pot odds to call?

Firstly, we need to calculate our odds of improving our hand.

From the chart above, we can see these odds are 6.67 to 1 (when having 6 outs).

Secondly, we have to determine our pot odds. Take the $500 from the main pot and add it to your opponents $100 bet. This gives us $600 that you could win by calling the $100 bet.

Therefore, your pot odds are 6 to 1.

Pot Odds: 6 to 1

Odds of Improving: 6.67 to 1

Because the number on the left (shown in bold) for pot odds is NOT larger than our odds of improving (6 ≯ 6.67), we do NOT have the expressed correct pot odds to call.

However, just because you don’t have the right pot odds to call doesn’t mean you should always fold your hand when facing that bet. Similarly, when you do have the right pot odds, it doesn’t mean that you should always call.

There are other considerations you should take into account before routinely throwing your hand into the muck.

Let’s briefly elaborate further on what some of these might be.

Additional Considerations

Calling On The Flop: Remember that if you call on the flop and don’t complete your draw on the turn, you could still face another bet on the turn. This scenario could affect how you use the “Rule of 2 and 4” in your calculations, as you wouldn’t see free river card in such instance as well.

Other Players Behind You: Other players still left to act may call, as well, or potentially even raise! If think they might call, you could take this into account in determining your pot odds to call. If you think they might raise, a fold might be the best play.

Fold Equity: Pot odds usually refer to whether or not calling on a draw is a profitable play. However, you must always balance your range and consider other possibilities, too – one of them being raising when the situation is right. This play is considered a “semi-bluff” where you can either win by (1) improving your hand on a later street; or (2) getting your opponent to fold immediately.

Implied Odds: Implied odds refers to how much money can be made on future rounds of betting if you do indeed complete your draw. For example, quite often, people with a straight or flush draw on the flop don’t have the correct expressed pot odds to call a bet profitably to see if they’ll complete their draw on the turn or the river. However, if they do complete their draw, they often rely on gaining another bet or two on future streets to make up the difference in calling without proper, expressed odds in the first place.

Discounted Outs: Sometimes, your opponents might need similar outs to improve their For example, if you have a draw to a baby flush, and your opponent has a draw to a bigger flush, this situation could prove detrimental to your bottom line. Sometimes, it’s good to take a conservative approach to counting your outs and arbitrarily discount some of them to account for this possibility. (For example, using 7 or 8 outs instead of the full 9 when calculating your odds for drawing to a flush.)

Equity vs. Villain’s Range: Pot odds vs. equity – it’s a concept that not all poker players are able to differentiate. While the term of “pot odds” refers to whether or not you’re getting the right price to call or not, equity refers to how much money of the pot should be yours based on your percentage to win the hand against a villain’s hand or hand range.

How to Calculate Pot Odds in Texas Hold'em

Throughout this article, we’ve illuminated a plethora of information on pot odds – what they are, the different types there are, how to calculate them, how to calculate your chances of improving, and how to relate these two figures together.

It’s now time to put everything you’ve learned into a few examples, specifically for Texas Hold’em.

Using pot odds in Texas Hold’em will certainly help you beat the tables. While No Limit Hold’em may use more implied odds principles (as you can stand to win much more by being able to freely choose exactly how much you want to bet or raise at any given point), Limit Hold’em uses the concept of expressed pot odds incredibly well!

We’ll illuminate two different examples of No Limit vs. Limit, specifically dealing with pot odds for a flush.

HAND EXAMPLES #3 / #4: Pot Odds To Call Flush Draw

You’re dealt KQ of Hearts. The board reads A-8-2-J with 2 hearts. There’s $60 in the pot. You and your opponent both have $200 remaining. Your opponent bets $20.

Do you have the right expressed odds to call? Implied odds?

How much additional money would you need to make on the river to profitably play this hand?

LIMIT HOLD’EM

NOTE: In Limit Hold’em, because there will be many players often playing each hand and calling small bets along the way, pots can get very bloated relative to the bets and betting limits as the betting rounds progress. This situation can give players correct odds to chase their draws, without even having to make additional money on future streets via implied odds.

Using the above information in the scenario, firstly, let’s calculate all the odds. We have a nut flush draw and a straight straw. 9 cards would give us a flush. Any of the 4 Tens would give us a straight. However, as we cannot count the Ten of Hearts twice, this gives us 12 outs to improve our hand with one card to come.

We multiply our outs by 2 to see our approximate percentage of winning the hand. This gives us 24% to improve to the winning hand (or about 3 to 1). As there’s now $80 in the pot after Villain’s $20 bet, we need to call $20 to win $80, giving us exactly 4 : 1 expressed odds on a call. In this scenario, we have exactly the right expressed odds to call.

In other words, even if we never gain an extra bet on the river from the times we call and improve, calling this $20 bet would still be a profitable play. We’d expect to gain an average of $6.67 for every time we call (plus whatever profits we could further extract on the river via implied odds)!

NO LIMIT HOLD’EM

Let’s make one slight change to the scenario described above. Instead of there being $40 in the pot, let’s say there’s only $20 when our opponent makes the $20 bet. Now we’d be getting 2 to 1 pot odds on a call (on a hand where we have 3 to 1 expressed odds).

In this new scenario, we can’t call based on expressed odds, but we can profitably call based on implied odds if we think we can get a certain amount of money from our opponent on the river for the times that our draw does come in.

Having a hand with expressed odds that give us 3 : 1 (where we win about 25% of the time) means that we’ll have to call the $20 bet now to potentially win 3 x $20 if our draw comes in on the river.

Therefore, if we ultimately can win at least $60 in total by calling the turn bet, this becomes a break-even (or profitable) call. With $40 in the pot before we call, we’d only need to win an additional $20 from our opponent on the river. If we do complete our draw and then bet $20, it would likely be difficult for our opponent to fold getting such good pot odds on the river.

The pot would be $60 (excluding our $20 bet), meaning they’d have to call $20 to win $80. In other words, they’d be getting 4 : 1 odds, and would only have to have the best hand 20% of the time for this river call to be profitable. This factor makes it likely that they'd call our bet for such a good price.

Chances are, though, that we could extract much more on the river from our opponent (as much as $30 or $45 into a pot of $60), making a turn call very profitable, based on implied odds.

How to Calculate Pot Odds in Omaha

Calculating pot odds in Omaha is a very similar endeavour to that in Texas Hold’em.

The biggest difference, however, concerns the outs:

You’re often going to have a lot more of them (outs) to improve your hand (from having multiple two-card hand combinations with your two extra hole cards). In fact, it’s not uncommon to have upwards of 20 outs that could improve your hand (even with two cards to come) with all of the “wraps” in Omaha.

You’re going to have to be wary of negative outs – outs that could improve your opponents hand to one better than yours!

Because of the increased number of hole card combinations (and chances that people will showdown much better hands than those typically found in Hold’em), you’re going to want draw to the nuts as much as possible.

HAND EXAMPLE #5:

You have Ah-Th-9c-8d. The flop comes 7h-6h-2c. Your opponent bets $100 into a $100 pot. You each have about $1,000. What should you do? Do you have the correct expressed/implied odds to call?

This hand is a very strong! While currently you only have Ace high, there is an incredible amount of cards (outs) that can help you improve to the nuts:

4 fives for the nut straight

3 eights for the nut straight

3 nines for the nut straight

3 tens for the nut straight

5 additional cards (excluding those above) that could give you a nut flush

You have a total of 18 outs to improve your hand! If you’re a player who is normally accustomed to playing Hold’em, you’ll likely find this number to be incredible!

Looking at our poker odds chart, we’ll see that with 18 outs and 2 cards to come, we have a 62% likelihood of improving our hand by the river! We’re even 38% likely to hit one of our draws just on the turn alone!

The only thing we’d have to worry about is an opponent having a set and the possibility of them boating up (improving to a full house). However, after the flop, even against many hand combinations even containing sets, we still have about a 50/50 chance of winning this hand (at worst)!

With the incredible odds we have of winning here, pot odds are almost irrelevant (except on a bricked turn). Instead, our focus should be on how can we extract the most money with the possibility of stacking someone!

As we have a 62% likelihood of winning, we have much better than the 2 to 1 odds we need to call. Perhaps, instead of simply calling here, though, to maximise our expected value with such a strong draw, maybe try raising!

The worst case scenario is that we’ll get it in against a set (which, as mentioned, we’re about 50/50). Raising also could draw in worse draws, pushing our likely profits even higher.

Summary: Why Calculate Pot Odds

Just as strategic people count cards in blackjack, using pot odds in poker will help you gain a strategic advantage over many of your lesser-skilled opponents. This strategy will help you reduce your losses and increase your profits while helping put you on the pathway to becoming a profitable player.

Sometimes when you play, you might not have the best pot odds to call (i.e. expressed odds), but in certain situations, there’s potential for you to make it up in future betting rounds by means of implied odds. Other times, you find yourself having to fold many of your weak draws simply because you don’t have much equity in the hand.

Ultimately, though, always remember that poker is a skill game that can be improved and developed over time. The more you try to use the poker skills you’ve learned here dealing with odds and outs, the more of a “feel” you’ll get for how they work and how to correctly use them in your gameplay.

In fact, before you know it, it’ll likely all come second nature to you!

All the best in using this newfound information, and good luck at the tables!